The Modelling of Ethernet Data and of Signals that are Heavy‐tailed with Infinite Variance*

We provide an overview of some of the research of the last ten years involving computer network data traffic. We describe the original Ethernet data study which suggested that computer traffic is inherently different from telephone traffic and that in the context of computer networks, self‐similar models such as fractional Brownian motion, should be used. We show that the on–off model can physically explain the presence of self‐similarity. While the on–off model involves bounded signals, it is also possible to consider arbitrary unbounded finite‐variance signals or even infinite‐variance signals whose distributions have heavy tails. We show that, in the latter case, one can still obtain self‐similar processes with dependent increments, but these are not the infinite‐variance fractional stable Lévy motions which have been commonly considered in the literature. The adequate model, in fact, can either have dependent or independent increments, and this depends on the respective size of two parameters, namely, the number of workstations in the network and the time scale under consideration. We indicate what happens when these two parameters become jointly asymptotically large. We conclude with some comments about high frequency behaviour and multifractals.     

李萨茹图形的几种实验方法

李萨茹图形在频率测量中有重要作用,本文总结了李萨茹图形的三种实验方法和特点,并简单介绍其应用.     

On-line control procedures under the random-walk model with measurement error and attribute observations

Assuming the quality characteristic process follows the random-walk model, the economic online control procedures are investigated by using the boundary correction technique when (1) the noise or measurement error follows either the random-walk model or the pure random model, and (2) the observations are taken by attributes only. Simple approximations for the long-run cost rate and optimal-control parameters are obtained.     

机载雷达平台运动补偿技术

机载雷达，由于平台运动造成地杂波谱产生多普勒频移和展宽。在讨论机载雷达地杂波频谱特性基础上，分析比较了ＡＭＴＩ系统和ＡＤＰＣＡ系统的性能，这些系统均具有良好的地杂波抑制能力。计算机模拟结果表明双路ＡＤＰＣＡ系统具有极好的地杂波抑制能力，是一种优异的平台运动补偿技术。     

Brownian矩阵环中的群逆与Drazin逆

本文指出了M．J．C．Gover关于Brownian矩阵环的群逆的一个错误，得到了矩阵A∈的群逆A#∈的充要条件．证明了，当A∈时，其Drazin逆A（d）∈，并给出了确定A（d）的一个算法．     

Distribution Planning to Optimize Profits in the Motion Picture Industry

We consider the distribution planning problem in the motion picture industry. This problem involves forecasting theater‐level box office revenues for a given movie and using these forecasts to choose the best locations to screen a movie. We first develop a method that predicts theater‐level box office revenues over time for a given movie as a function of movie attributes and theater characteristics. These estimates are then used by the distributor to choose where to screen the movie. The distributor's location selection problem is modeled as an integer programming‐based optimization model that chooses the location of theaters in order to optimize profits. We tested our methods on realistic box office data and show that it has the potential to significantly improve the distributor's profits. We also develop some insights into why our methods outperform existing practice, which are crucial to their successful practical implementation.     

后发工业国技术从模仿到创新的路径、动力与选择机制——基于汽车产业拉美模式、日韩模式和中国模式的比较分析

后发工业国从模仿到创新的技术战略演进路径呈现多样性,为解释后发工业国汽车产业技术演进路径差异和选择,通过构造一个以企业家精神和企业技术能力成长为主要内驱力,市场需求、技术发展和溢出为拉力、研发投入和产业激励政策为推力,高昂技术学习成本和企业创新惯例和惰性等为阻力以及市场竞争和约束性产业政策为压力的汽车产业技术演进动力模型,比较分析了后发工业国汽车产业技术演进的动力差异和选择机制,并为中国汽车产业技术能力的发展提供有益建议。     

Pfeifer records process

In this article, we study the limit distribution of sums of Pfeifer records. Motivated by the results obtained by Arnold and Villaseñor [Generalized order statistics process and Pfeifer records, Statistics 46(3) (2012), pp. 373–385], we show that the partial sum process of Pfeifer records converge to a function of the Brownian motion. The normalization is either a sequence of appropriate constants or a sequence of functions, depending on the tail behaviour of the underlying variables. These results, in particular, prove stronger version of results obtained in Villaseñor and Arnold [On limit laws for sums of Pfeifer records, Extremes 10 (2007), pp. 235–248] and Bose and Gangopadhyay [Convergence of linear functions of Pfeifer records, Extremes 13 (2010), pp. 89–106] and extends results of Bose et al. [Partial sum process for records, Extremes 8 (2005), pp. 43–56] from classical records to Pfeifer records.     

Tail asymptotic of Weibull-type risks

With motivation from Arendarczyk and De¸bicki [Asymptotics of supremum distribution of a Gaussian process over a Weibullian time. Bernoulli. 2011;17:194–210], in this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer [The weak tail dependence coefficient of the elliptical generalized hyperbolic distribution. Extremes. 2012;15:159–174] and Bose et al. [Product of exponentials and spectral radius of random k circulants. Annales de l'Institut Henri Poincare Probabilites et Statistiques. 2012;48:424–443].     

On the Diffusion Coefficient: The Einstein Relation and Beyond

We present a detailed derivation of the closed-form expression for the diffusion coefficient that was initially obtained by Einstein.[4] in press.  [Google Scholar] The present derivation does not make use of a fictitious force as did the original Einstein derivation, but instead concentrates directly on establishing a dynamic equilibrium between the forces of pressure and friction acting on a Brownian particle. This approach makes it easier to understand the true essence of the argument, and thus makes it simpler to apply the argument in a more general case or setting. We demonstrate this by deriving the equation of motion of a Brownian particle that is under the influence of an external force in the fluid with a non-constant temperature. This equation extends the well-known Smoluchowski approximation[24] Smoluchowski, M. von. 1915. Über Brownsche Molekularbewegung unter Einwirkung äußerer Kräfte und deren Zusammenhang mit der verallgemeinerten Diffusionsgleichung. Ann. Phys., 48: 1103–1112.  [Google Scholar] to the case of non-constant temperature, and offers new insights into the Ludwig–Soret and Enskog–Chapman effects (providing also a scholar example explaining the need for a stochastic integral). The key point in the derivation is reached by applying the Einstein dynamic equilibrium argument together with the conservation of the number of particles law. We show that this approach leads directly to the Kolmogorov forward equation whenever the setting is Markovian. The same method can also be applied in the case of interacting Brownian particles satisfying the van der Waals equation. In this setting we first demonstrate that the presence of short-range repulsive forces between Brownian particles tends to increase the diffusion coefficient, and the presence of long-range attractive forces between Brownian particles tends to decrease it. The method of derivation then leads to a nonlinear partial differential equation which in the case of weak interaction reduces to the Fokker–Planck equation. One of the main aims of the present article is to demonstrate that the Einstein argument leads to a truly dynamical theory of diffusion.